To Infinity But No Further

Wow, infinity right? 
We are living in, when last checked, an infinite universe. You might think this is just another scaremongering pop-up theory formed by the Tory government (under Thatcher) to keep us from worrying about house prices. But no, scientists (I'll check which ones in a minute) maintain (endlessly of course) that the universe goes on for ever. Let us for the sake of argument agree with them.

From Wikipedia:
In 1584, the Italian philosopher and astronomer Giordano Bruno proposed an unbounded universe in On the Infinite Universe and Worlds: "Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds."

So if you have an infinite universe, there is not only one other sun like ours, but an infinite number of suns exactly like ours, with exact replicas of Earth revolving around them. 

A similar theory involves pi. Again, from Wikipedia:

The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.141592. Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π. Consequently its decimal representation never ends and never settles into a permanent repeating pattern. 

You can argue that pi isn't really a number, but an idea of a number. But if it is a number, it's an infinite one. As a result all number sequences must appear in it. For instance: take all the phone numbers in the Yellow Pages, string them end-to-end, and this sequence will be in pi. One business in the book goes under, their number is removed, the new sequence will still eventually appear in pi. 

Now fingerprints.
Everyone knows that every human's fingerprints are unique. But this can only be a theory because not everyone has been born yet and not everyone's fingerprints have been checked. Similarly, it might take a while, but two identical snowflakes might turn up: "Quick, Madge! Get the microscopic camera, it's melting." etc. Perhaps stretching a point; Mike Silverman (who introduced the first automated fingerprint detection system to the Metropolitan Police) has his doubts about the theory too. To be fair however, he is factoring human error into the equation:
From The Telegraph...

So which one of these theories should we believe? None of them are religious or creationist mumbo-jumbo. They're like evolution, making sense but also making you stare off into space when you should be concentrating on work or whatever.

But they can't all be right. 

If all fingerprints are different, then all the planets and stars in the universe can be different too. If all snowflakes are unique, then all the numbers in pi can be random and follow no other sequence. If someone finds two sets of similar dabs then we are not alone.

And then there's God.
Another infinite concept, he/she has to keep an eye on everything ALL the time while creating new stuff in the process; it must be infinitely exhausting. When asked what his religious beliefs were, the writer and all-round good egg Frank Muir replied: "I'm a lapsed agnostic - my doubts are beginning to waver." How can an atheist explain the universe if he can't believe it's infinite? Must he downgrade to agnosticism? Unfortunately for those reading this, neither of you will reach far enough into space to take a picture of The Restaurant At The End Of The Universe. And the other one is unlikely, let us be frank, to bump into God at Tesco. 

Blaise Pascal tried to work out what was the best philosophy to live by, given the fact that we don't know what will happen to us at the end:

From Wikipedia once more:
'Pascal's Wager' is an argument in apologetic philosophy which was devised by the seventeenth-century French philosopher, mathematician, and physicist Blaise Pascal (1623–1662). It posits that humans all bet with their lives either that God exists or not. Given the possibility that God actually does exist and assuming an infinite gain or loss associated with belief or unbelief in said God (as represented by an eternity in heaven or hell), a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.).

So be nice and you might be rewarded later with infinite fun in Heaven, or have all the fun now and risk infinite nasties. You do the maths.

Any comments welcome....

"John Davies ‏@artfulbooks  I reckon any number also has infinite potential, so Pi can go on indefinitely without hesitation, deviation or repetition. Irrational numbers do my 'ead in. 
And what about those frogs jumping half way to a wall and never reaching it? #strewth"

Even 1 can be an infinite number if you give it enough decimal places: 1.0000000000000000000000000000000000000000000... (I could go on)

The experiment John refers to is this: 

Place a frog a foot away from a wall and ask it to jump half way. Then tell it to jump half way again; will froggy ever reach the wall? If the frog keeps jumping, it must eventually reach the wall. There's a formula for working out why the frog must reach the wall: on one side you have the distance jumped in fractions "1/2, plus 1/2 squared" and so on. These distances equal 1, which is the original distance to travel. 

But, just saying all those fractions = 1 doesn't prove that the frog reaches the wall! If it is only jumping half way it will never be closer than half of any distance, no matter how small. Show us, clever cloggs! First of all, I'm on to the RSPCA - why not try it with an inanimate object? Something you can control? Or are you worried that it won't work and you made up the story of the frog to cloud the issue. Also what if, like a piece of A4 paper, you reach a point where you can no longer halve the space between the frog and the wall? The frog will be sitting there drumming its fingers, waiting for the next leap, NOT at the wall.
Mathematicians: don't trust them.

Peter G. Casazza writes: (on this and other, possibly crackpot, maths problems)

I maintain that Casazza is wrong. The frog doesn't reach the wall because eventually the space between the frog and the wall will be too small to halve. If the frog decides to jump on, into the wall, it will be of its own free will and nothing to do with Peter G. #FreeTheFrog